# Bifurcations analysis of turbulent energy cascade

## Abstract

This note studies the mechanism of turbulent energy cascade through an opportune bifurcations analysis of the Navier–Stokes equations, and furnishes explanations on the more significant characteristics of the turbulence. A statistical bifurcations property of the Navier–Stokes equations in fully developed turbulence is proposed, and a spatial representation of the bifurcations is presented, which is based on a proper definition of the fixed points of the velocity field. The analysis first shows that the local deformation can be much more rapid than the fluid state variables, then explains the mechanism of energy cascade through the aforementioned property of the bifurcations, and gives reasonable argumentation of the fact that the bifurcations cascade can be expressed in terms of length scales. Furthermore, the study analyzes the characteristic length scales at the transition through global properties of the bifurcations, and estimates the order of magnitude of the critical Taylor-scale Reynolds number and the number of bifurcations at the onset of turbulence.

- Authors:

- Publication Date:

- OSTI Identifier:
- 22447621

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Annals of Physics; Journal Volume: 354; Other Information: Copyright (c) 2015 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BIFURCATION; LYAPUNOV METHOD; NAVIER-STOKES EQUATIONS; REYNOLDS NUMBER; TURBULENCE; WASTE HEAT UTILIZATION

### Citation Formats

```
Divitiis, Nicola de, E-mail: n.dedivitiis@gmail.com.
```*Bifurcations analysis of turbulent energy cascade*. United States: N. p., 2015.
Web. doi:10.1016/J.AOP.2015.01.017.

```
Divitiis, Nicola de, E-mail: n.dedivitiis@gmail.com.
```*Bifurcations analysis of turbulent energy cascade*. United States. doi:10.1016/J.AOP.2015.01.017.

```
Divitiis, Nicola de, E-mail: n.dedivitiis@gmail.com. Sun .
"Bifurcations analysis of turbulent energy cascade". United States.
doi:10.1016/J.AOP.2015.01.017.
```

```
@article{osti_22447621,
```

title = {Bifurcations analysis of turbulent energy cascade},

author = {Divitiis, Nicola de, E-mail: n.dedivitiis@gmail.com},

abstractNote = {This note studies the mechanism of turbulent energy cascade through an opportune bifurcations analysis of the Navier–Stokes equations, and furnishes explanations on the more significant characteristics of the turbulence. A statistical bifurcations property of the Navier–Stokes equations in fully developed turbulence is proposed, and a spatial representation of the bifurcations is presented, which is based on a proper definition of the fixed points of the velocity field. The analysis first shows that the local deformation can be much more rapid than the fluid state variables, then explains the mechanism of energy cascade through the aforementioned property of the bifurcations, and gives reasonable argumentation of the fact that the bifurcations cascade can be expressed in terms of length scales. Furthermore, the study analyzes the characteristic length scales at the transition through global properties of the bifurcations, and estimates the order of magnitude of the critical Taylor-scale Reynolds number and the number of bifurcations at the onset of turbulence.},

doi = {10.1016/J.AOP.2015.01.017},

journal = {Annals of Physics},

number = ,

volume = 354,

place = {United States},

year = {Sun Mar 15 00:00:00 EDT 2015},

month = {Sun Mar 15 00:00:00 EDT 2015}

}